Viscous fingering in self-affine Sierpinski carpet

In this paper, the self-affine Sierpinski carpet is constructed. The viscous fingering (VF) in self-affine Sierpinski carpet, based on the assumption that bond: radii are truncated Rayleigh distribution, is simulated by means of successive over-relaxation techniques. The fractal dimension of VF is calculated. The results show that the VF pattern of self-affine Sierpinski carpet in the limit viscosity ratio M --> infinity is found to be similar to the DLA pattern. When M = 1, the interior of the cluster of the displacing fluid is compact and the displacement process is stable for long length scales.